Graph, transform, and solve absolute value functions, and apply them to model real-world distance and tolerance scenarios.

Multiply trinomials by binomials and trinomials, simplify expressions with multiple operations, and apply polynomial operations to real-world problems.

Recognize hidden structure—quadratic forms, higher-degree polynomials, and rational expressions—and combine multiple structural patterns to rewrite complex expressions equivalently.

Understand equality, translate words to expressions, and simplify expressions using properties and combining like terms.

Derive and apply algebraic identities for binomial squares, difference of squares, and binomial cubes to simplify and expand expressions.

Identify and distinguish the structural parts of algebraic expressions, including terms, factors, and coefficients.

Apply quadratic equations to real-world problems, use the discriminant to analyze roots, and construct quadratic equations from given information.

Choose the best method to solve quadratics, use the discriminant, and apply these skills to word problems and mixed practice.

Distinguish rational from irrational numbers, represent them as fractions and decimals, and classify numbers within the hierarchy of the real number system.

Prove that sums and products of rational numbers are rational, explain why operations involving irrationals yield irrational results, and determine closure properties of number sets.